Digital Electronics: Number Representation

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Questions and Answers

What is the main advantage of using a high precision format in floating point arithmetic?

It results in more accurate calculations. (correct)

It speeds up processing time.

It reduces memory consumption.

It simplifies the arithmetic operations.

How many bits are allocated for the exponent in single precision format?

11 Bits

23 Bits

8 Bits (correct)

1 Bit

In the IEEE 754 standard, how many bits are used for the sign in double precision format?

52 Bits

1 Bit (correct)

64 Bits

23 Bits

Which of the following is NOT a feature of the IEEE 754 floating point standard?

Requires all computations to be in decimal format. Signup and view all the answers

What is the total number of bits used in double precision floating point representation according to IEEE format?

64 Bits Signup and view all the answers

What is the significance of the Most Significant Digit (MSD) in a binary number?

It is the left-most symbol of the binary number. Signup and view all the answers

In binary to decimal conversion, what does the least significant digit represent?

The right-most symbol contributing the least value. Signup and view all the answers

How many bits are typically contained in a byte?

8 bits Signup and view all the answers

What term is used to refer to a grouping of 4 bits?

Nibble Signup and view all the answers

What does the term 'Word' typically refer to in a computing context?

16 bits Signup and view all the answers

What is the smallest grouping of bits in a computer system?

Bit Signup and view all the answers

Which of the following correctly identifies a factor that influences how information is stored in a computer system?

The architecture of the PC. Signup and view all the answers

Which statement about binary digits (bits) is incorrect?

Bits can only represent decimal values. Signup and view all the answers

What does the '-' sign in front of a number signify?

It identifies the number as a negative value. Signup and view all the answers

What is the binary range for an unsigned representation with 'n' bits?

0 to $2^n - 1$ Signup and view all the answers

How does the term 'Kilo' differ in binary compared to decimal?

Kilo is equal to $2^{10}$ = 1024 in Binary. Signup and view all the answers

What is the relationship between Mega and Kilo in binary representation?

Mega is equal to $Kilo^2$. Signup and view all the answers

What value does Giga represent in relation to Kilo in binary?

Giga is $Kilo imes Mega$. Signup and view all the answers

What does the weight of the right-most digit in the decimal system correspond to?

1 Signup and view all the answers

How does the weighting of digits change as you move from right to left in a decimal number?

Weights increase by a factor of 10 Signup and view all the answers

What is the highest symbol used in the binary number system?

1 Signup and view all the answers

What is the base (radix) of the decimal number system?

10 Signup and view all the answers

Which symbols are unique to the decimal system?

0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Signup and view all the answers

What is the decimal equivalent of the binary number 01011010?

90 Signup and view all the answers

In the binary representation scheme, what weight does the left-most digit of the number 01011010 carry?

64 Signup and view all the answers

Which statement accurately describes the symbols used in the binary number system?

They are limited to 0 and 1. Signup and view all the answers

What is the decimal equivalent of the hexadecimal number 9AC16?

2476 Signup and view all the answers

How many bits does a single hexadecimal digit represent when converting binary to hexadecimal?

4 bits Signup and view all the answers

What is the result of converting the binary number (110101111)2 to hexadecimal?

1AF Signup and view all the answers

In binary to hexadecimal conversion, which method is used to group binary digits?

In groups of 4 Signup and view all the answers

What is the final result when converting the binary number 137110 using the hexadecimal conversion method shown?

55B16 Signup and view all the answers

What is the correct binary equivalent of the hexadecimal digit 'A'?

1010 Signup and view all the answers

When converting the decimal number 2476 to hexadecimal, what is the correct representation?

9AC Signup and view all the answers

Which part of the conversion process from binary to hexadecimal helps in simplifying binary representation for humans?

Reducing the number of digits Signup and view all the answers

What is the first step to find the two's complement of a negative number?

Invert all '1's to '0's and '0's to '1's. Signup and view all the answers

When adding two numbers using two's complement, what does a most significant bit of '1' in the result indicate?

The answer is negative. Signup and view all the answers

In the example of subtracting 25 - 7, what is the two's complement representation of -7?

11111001 Signup and view all the answers

What must be true about the operands when performing two's complement addition?

They must have the same number of bits. Signup and view all the answers

When you convert a negative number to two's complement, what should you do after inverting the bits?

Add 1 to the inverted bits. Signup and view all the answers

What is the binary result of adding 25 and -7 using two's complement?

00010010 Signup and view all the answers

What do you do to verify the result of a two's complement addition if the answer is negative?

Change all ones to zero, zeros to one, and add one. Signup and view all the answers

Which statement is true regarding the use of two's complement?

It is used to represent both positive and negative numbers. Signup and view all the answers

Study Notes

Lecture 1: Number and Data Representation

Digital electronics represent values using discrete values of physical quantities (e.g., electricity)
Analogue signals represent information as a continuously variable physical quantity (e.g., sound, light)
Digital systems use internal representation for all information stored, including numerical data and character strings
The decimal system uses digits 0-9, with each digit's position assigned a weight based on powers of 10, increasing leftward. For example, in 331, the rightmost 1 has a weight of 10⁰ = 1, the middle 3 has a weight of 10¹ = 10, and the leftmost 3 has a weight of 10² = 100, resulting in a value of 300+30+1
The binary system uses only 0 and 1 with weights based on powers of 2.
The hexadecimal system uses 0-9 and A-F, with A equaling 10, B equaling 11,.. and F equaling 15, using powers of 16.
Octal uses digits 0-7 using powers of 8.
A Byte is 8 bits, a Word is 16 or more bits, and nibbles are half a byte (4 bits)
Unsigned numbers only have magnitude, e.g., 27
Signed numbers use a sign (e.g., + or -) to indicate the direction of magnitude. -27
Signed magnitude, one bit denotes sign the remaining bits denote magnitude
Two's complement allows computers to perform subtraction by treating it as addition of the 2's complement of the second number.
Floating-point numbers use a mantissa and exponent to represent fractional values. This allows for the representation of very large or small numbers by shifting the decimal point to a different location.
IEEE 754 is the most common standard for handling floating-point numbers; this is for better data accuracy. Single-precision uses 32 bits, and double-precision uses 64 bits to store floating-point data.

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Description

Explore the fundamental concepts of number and data representation in digital electronics. This quiz covers various systems including decimal, binary, hexadecimal, and octal, alongside byte and word definitions. Test your understanding of how values are represented in both digital and analogue formats.